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Someone posted the solution, but the post disappeared while I was reading it. I guess he deleted it? Glad I was able to remember what he said.

I copied the smoke image with the black background, pasted it into a new layer on the main image I'm working on, and changed the layer to "Lighten" and it looks perfect. A little hackish with the copy/paste from another file part, but it looks great.

Thanks to everyone who helped.